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Optimal asymptotic quadratic error of density estimators for strong mixing or chaotic data

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  • Bosq, Denis

Abstract

Under mild mixing conditions, we show that the kernel density estimator has exactly the same asymptotic quadratic error as in the i.i.d. case. Curiously, that result remains almost valid if the data are chaotic.

Suggested Citation

  • Bosq, Denis, 1995. "Optimal asymptotic quadratic error of density estimators for strong mixing or chaotic data," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 339-347, March.
    • Handle: RePEc:eee:stapro:v:22:y:1995:i:4:p:339-347
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    References listed on IDEAS

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    1. Vieu, Philippe, 1991. "Quadratic errors for nonparametric estimates under dependence," Journal of Multivariate Analysis, Elsevier, vol. 39(2), pages 324-347, November.
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    Cited by:

    1. Michel Harel & Jean-François Lenain & Joseph Ngatchou-Wandji, 2016. "Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 296-321, June.
    2. D. Blanke & D. Bosq & D. Guégan, 2003. "Modelization and Nonparametric Estimation for Dynamical Systems with Noise," Statistical Inference for Stochastic Processes, Springer, vol. 6(3), pages 267-290, October.
    3. N. Hosseinioun & H. Doosti & H. Nirumand, 2012. "Nonparametric estimation of the derivatives of a density by the method of wavelet for mixing sequences," Statistical Papers, Springer, vol. 53(1), pages 195-203, February.
    4. Biau, Gérard, 2002. "Optimal asymptotic quadratic errors of density estimators on random fields," Statistics & Probability Letters, Elsevier, vol. 60(3), pages 297-307, December.
    5. Leblanc, Frédérique, 1996. "Wavelet linear density estimator for a discrete-time stochastic process: Lp-losses," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 71-84, March.

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